Power series for integral (1/x) dx

[Jbreezy]

Homework Statement

I have to find the power series representation for integral (1/x) dx

Homework Equations

ln (1+x)

The Attempt at a Solution

This is very similar to ln(1+x) but I don't know if this helps me.

Is this ln(x) shifted one to the right? So maybe I can use what is already the power series for ln(1+x) = Ʃ (-1)^(n-1) (x^n)/n from n = 1 to ∞

so could I do ln(x) = [(-1)^(n) (x^(n+1)] / (n+1)

NO? Maybe I shifted it wrong?

 

[Mark44]

Homework Statement

I have to find the power series representation for integral (1/x) dx

Homework Equations

ln (1+x)

The Attempt at a Solution

This is very similar to ln(1+x) but I don't know if this helps me.

$\int \frac{dx}{x} = ln(x) + C$, assuming x > 0.

ln(x + 1) is the translation by one unit left, not right, of the graph of y = ln(x).

Is this ln(x) shifted one to the right? So maybe I can use what is already the power series for ln(1+x) = Ʃ (-1)^(n-1) (x^n)/n from n = 1 to ∞

so could I do ln(x) = [(-1)^(n) (x^(n+1)] / (n+1)

NO? Maybe I shifted it wrong?

 

[Jbreezy]

OK so this

Ʃ (-1)^(n-1) (x^n)/n from n = 1 to ∞

Should be Ʃ (-1)^(n-2) (x^(n-1))/(n-1) from n = 1 to ∞

Right?

 

[Mark44]

OK so this

Ʃ (-1)^(n-1) (x^n)/n from n = 1 to ∞

Should be Ʃ (-1)^(n-2) (x^(n-1))/(n-1) from n = 1 to ∞

Right?

Instead of writing "answers" show me some mathematics reasoning.